I'm still using an old DSC-P72 I picked up 5+ years ago for about $110, and aside from the low ISO, I've found its image quality a lot better than any of the low-end cameras I've seen and tried in retail chains these days in the $90-160 price range. Everything inexpensive now seems to have really bad CCDs, bad optics, bad firmware, etc. with inflated megapixel claims to make them look attractive.

I also do a good bit of photography in places where electricity to charge proprietary-form-factor batteries is not readily available, but I can carry a lot of rechargeable AA's or pick up throw-away AA's locally in a pinch, so I'm especially looking for cameras with AA batteries.

Is there any hope of finding a modern camera of similar or better quality to what I have now, or is the market just full of junk these days unless you move to a higher price range?

In my opinion, almost everything produced today is of higher quality then the P72 that you have. I am very familiar with that model, and it wasn't even above average in its day. FYI it is from 2003, so if you picked it up 5-6 years ago, it was already old. If you are testing out these models in the store and assume bad CCD, optics and firmware from observations made at that time, I think you should take one home and use it instead.
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dpollittMay 4 '11 at 18:24

That's a little above the price range I was looking at, but it sure is impressive! Actually Canon's one of the few brands I've seen some ok cheap cameras from, but the best among them was an older model (can't remember it right off) that may be discontinued now...
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R..May 4 '11 at 0:47

To start there are unfortunately less and less camera models that run on AA batteries. Here is the complete list. If you look at the breakdown, most of them are compact or ultra-zooms.

The compacts are mostly generic but there are some stand-out models. One is the Canon Powershot SX130 which has full manual controls and a stabilized wide-angle 10X optical zoom. Image quality is good but for its price.

The ultra-zooms are larger and a few models use CMOS sensors but will cost you 2 or 3 times more compared to the SX130. That will improve quality a little but certainly not by the same factor as the cost.

Better image quality in a fixed-lens camera comes from cameras with larger sensors, all of which use proprietary batteries and cost noticeably more.

The Panasonic Lumix DMC-FH20K is an excellent camera that just matches your $160 price range. Unfortunately for you it does use a Li-Ion battery pack. I would grab this model and head to ebay for a handful of off brand batteries for extremely cheap. If you don't have an issue with carrying a ton of AA's, then I don't see why this wouldn't work either.